At the risk of being a cynic with no better plan I'm putting forward a criticism with no alternative. Calvin's theory of penal substitutionary atonement has bothered me for years. It gets brought out over and over, not just as the explanation for Jesus' death but as a necessary statement of faith for the believer. If I'm to hold to it, then I should confess that I deserve eternal damnation, and that my only way out of it is for someone sufficiently better than me (i.e. Jesus) to be punished on my behalf.
This atonement requires that God receives satisfaction, and the only satisfaction that God will accept is eternal damnation. In this model, God needs to administer punishment to fit the crime and is bound by that need; God is captive to the requirement for punishment.
And yet, God forgives. Jesus taught that God forgives. Jesus gave authority to his disciples to forgive sins. But what is forgiveness? Forgiveness is a restoration that relinquishes the obligation to make restitution or to administer punishment. If I forgive you, then I let go of any claim that you make things right.
Forgiveness is not penalty. Forgiveness is the acceptance of the other, despite any wrongs or injustice. Conversely, penalty demands reparation.
I think that there is a conflict between penalty and forgiveness. It seems to me that the teaching of Jesus was heavily in favour of forgiveness and so I'm skeptical of Calvin's theory of penal substitutionary atonement.
Note to evangelical readers
Please don't be offended by this. There have been centuries of attempts to develop a model of the atonement. The most popular evangelical model (Calvin's) is only five hundred years old. It's not "the one true interpretation" of the matter.